Question

Use function composition to determine if f(x) and g(x) a f(x)=-x+1 and g(x)=(x-1)/(2)

Answer 1

To determine f(x) and g(x) using function composition, we substitute g(x) into f(x) to get f(g(x)) = -x/2 + 3/2.

Step-by-step explanation:

To determine f(x) and g(x) using function composition, we substitute g(x) into f(x). First, we substitute x with g(x) in f(x) = -x + 1:

f(g(x)) = -g(x) + 1

Next, we substitute g(x) with its expression (x-1)/2:

f(g(x)) = -((x-1)/2) + 1

Simplifying this expression, we can multiply both terms by 2 to eliminate the fraction:

f(g(x)) = (-x + 1)/2 + 1

f(g(x)) = -x/2 + 3/2